A Lorentz tube is Lorentz gas in a d-dimensional set which is infinitely extended in one dimension only (e.g., a strip in d = 2, a square cylinder in d = 3, etc.). One expects that, in great generality, a system like this possesses strong chaotic properties—whatever this means for dynamical systems preserving an infinite measure. At the very least, the typical Lorentz tube should be recurrent. By randomly placing scatterers within the tube, in a natural way, we construct ensembles of (deterministic) dynamical systems. In other words we define quenched random Lorentz tubes. Under some general hypotheses (very mild for d = 2; a little stronger for d > 2) we prove that every system in the ensemble is uniformly hyperbolic and almost every system is recurrent, ergodic, and such that the first-return map to any given scatterer is K-mixing.

(Joint papers with G. Cristadoro, M. Seri, M. Degli Esposti, S. Troubetzkoy.)